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Title
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Fischer decomposition for osp(4|2)-monogenics in quaternionic Clifford analysis
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Author
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Abstract
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| Spaces of spinor-valued homogeneous polynomials, and in particular spaces of spinor-valued spherical harmonics, are decomposed in terms of irreducible representations of the symplectic group Sp(p). These Fischer decompositions involve spaces of homogeneous, so-called osp(4|2)-monogenic polynomials, the Lie super algebra osp(4|2) being the Howe dual partner to the symplectic group Sp(p). In order to obtain Sp(p)-irreducibility, this new concept of osp(4|2)-monogenicity has to be introduced as a refinement of quaternionic monogenicity; it is defined by means of the four quaternionic Dirac operators, a scalar Euler operator E underlying the notion of symplectic harmonicity and a multiplicative Clifford algebra operator P underlying the decomposition of spinor space into symplectic cells. These operators E and P, and their Hermitian conjugates, arise naturally when constructing the Howe dual pair osp(4|2)xSp(p), the action of which will make the Fischer decomposition multiplicity free. Copyright (c) 2016 John Wiley & Sons, Ltd. |
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Language
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English
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Source (journal)
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Mathematical methods in the applied sciences. - Stuttgart
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Publication
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Stuttgart
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2016
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ISSN
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0170-4214
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DOI
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10.1002/MMA.3910
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Volume/pages
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39
:16
(2016)
, p. 4874-4891
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ISI
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000385719500020
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Full text (Publisher's DOI)
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